Question

factor the trinomial completely.

(x^2 + 4x - 32)

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. (x^2 + 4x - 32 = )
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

We need to factor the trinomial:

$$ x^2 + 4x - 32 $$

Identify the values of \( b \) and \( c \):

$$ b = 4 $$

$$ c = -32 $$

Step 2: Find factors

Find two integers that multiply to \( -32 \) and add up to \( 4 \).

Factors of \( -32 \):

$$ 8 \times (-4) = -32 $$

$$ 8 + (-4) = 4 $$

The two numbers are \( 8 \) and \( -4 \).

Step 3: Write factored form

Write the trinomial as a product of two binomials:

$$ (x + 8)(x - 4) $$

Answer:

A. \( x^2 + 4x - 32 = (x + 8)(x - 4) \)